Therefore, one trivial \(\widetilde{K}\) -type lives in the even part of \(H_D(\pi )\) ,
while the other lives in the odd part of \(H_D(\pi )\) . See Lemma 2.3 of [1]}. As a consequence, the Dirac index of \(\pi \)  vanishes.
Note that \({\rm DI}(\pi )\)  can also be easily calculated by atlas using [2]} (certain outputs are omitted):
